A question about the information loss paradox

[kdv]

In the information loss paradox, people say that in quantum mechanics , time evolution is unitary. They usually do not say anything about the measurement process of if they do, they briefly say that the measurement process does not violate unitarity either if one takes into account the measuring device . I am guessing they mean by that that the measuring process amounts to entangling the observed state with the measuring device. But I thought that this was controversial, that it assumes a many-world type of interpretation of QM. If I measure the spin of a particle, say, and I get a certain result, surely I cannot deduce the state of the particle before the measurement (other than being able to say that the particle has a nonzero component of the eigenstate corresponding to my measurement).

So what do they mean by saying that in QM, time evolution is *always* unitary??

 

[Fra]

So what do they mean by saying that in QM, time evolution is *always* unitary??

There are multiple ways to approach and "analyse" this, depending on what point you want to make (illustrated the paradox or resolve it).

My preferred quick comments would be these:

Quantum mechanics, by definition, only predicts the time evolution of the information state relative a given obserer state in between observations.

This evolution pretty much follows from conservation of information. And information is conserved by definition, as new information ONLY enters during measurements. The observers only source of information is by interacting with tis environment.

Then, what is mean by unitary evolution during a measurement? Well that is a confuesed terminology IMO. What you CAN do is to consider another observer, that observer the original "observer+system", sometimes you say instead "measurementdevice+system", but i think that is less clean. But the idea is the measurement devices is the physical sensor part of observer in a way. But the latter easily looses track of where history of interactions(sometimes called preparations) is stored.

Anyway, in the view of this second observer, the measurement process in the view of the first observer is indistinguishable from an "internal interaction", and if we can only find the hamiltonian, then this is unitary as well. So there is no contradiction.

But this isn't the end of story imo, because it is not a viable "strategy" to keep looking at larger and larger observers. Thisi s exactly why the "observer" gets pushed into the infinite boundary of the system. Soemtimes we need an inside observer view.

Also even in the boundary observer picture, we have the problem of inferring the "internal interactions" from a give perspecting, using only measuments!

If you follow my reasoning the conclusion is: to understand the internal interactions and structure of matter - is indistinguishable from understanding the measurement process from the inside view.

/Fredrik

 

[tom.stoer]

In the information loss paradox, people say that in quantum mechanics , time evolution is unitary. They usually do not say anything about the measurement process or if they do, they briefly say that the measurement process does not violate unitarity either if one takes into account the measuring device ... But I thought that this was controversial, that it assumes a many-world type of interpretation of QM ...So what do they mean by saying that in QM, time evolution is *always* unitary??

I cannot say what "they" mean.

For me there are basically two options.

1) If you look at the fundamental axioms of quantum mechanics in many cases "measurement" is mentioned but not defined, or it is defined w.r.t to some external observer. IMHO all these scenarios are dead ends when talking about unitarity being universal.

2) So yes, you are right, the only way out (for me) is that quantum mechanics applies to the whole universe w/o ever introducing any entity not being part of the system or not being subject to unitary time evolution of the system. And one must ban the term "measurement" from the axioms. If we want to talk about "measurement being unitary" this means that "measurement" is a process complying with unitary time evolution as usual. So "measurement" is nothing else but a specific (unitary) interaction which imprints a kind of branching structure according to decoherence which stays in place w/o any collapse, projection postulate or Heisenberg cut. This is essentially "Many-Worlds" from a modern (decoherence) perspective.

My persuasion is that either we believe in universal unitarity, then we must subscribe to some "Many-Worlds" type of interpretation according to (2), or we do not like this conclusion, then we must not talk about universal unitarity but restrict ourselves to "universal unitary time evolution excluding the not well understood measurement process itself".

(there is a third option - as usual - namely shut-up-and-calculate)

 

[Fra]

or we do not like this conclusion, then we must not talk about universal unitarity but restrict ourselves to "universal unitary time evolution excluding the not well understood measurement process itself".

I for one do not see a true unitarity as a valid premise beause it is not even inferrable in principle by a real observer or by a real scientist. Also the whole notion of a state of the entire universe - including the obsever is too speculative and imho.

But even so, a fapp kind of unitarity should in principle be applicable to for example small microscopic black holes on Earth because the "external observer" is the vastly more complex and thus stands at chance to inprinciple encode the statevector beyond the boundary.

So i am convinced that one can not speak of this generally as bh paradox as i think unitarity is only fapp recoverable when the mass od the bh is very small as compare to the observer system.

So i am convinced that tricks that works for microscopic bh as seen in a lab, will not work for real massive bh in space as seen from earth. Ie. Randomness from a small bh or bh remnant of a largr bh are mosy likely different than a large bh.

As long as we don't see the difference we are imo not seeing the lmportancr of what i personally se as the hearr of measurement theory.

So i opt for denying a fundamental unitarity and embrace the measurement problem... and insist we neeed to solve it by reconstucting qm rather than finding workarounds.

/Fredrik

 

[tom.stoer]

I for one do not see a true unitarity as a valid premise beause it is not even inferrable in principle by a real observer or by a real scientist. Also the whole notion of a state of the entire universe - including the obsever is too speculative and imho.

That is a valid position - but not the only one. Platonists think different.

But even so, a fapp kind of unitarity should in principle be applicable to for example small microscopic black holes on Earth because the "external observer" is the vastly more complex and thus stands at chance to inprinciple encode the statevector beyond the boundary.

FAPP is of course a valid position, but does not comply with "always" or "universal".

So i opt for denying a fundamental unitarity and embrace the measurement problem... and insist we neeed to solve it by reconstucting qm rather than finding workarounds.

Why not take Everett's view as fundamental hypothesis, work on it and try to falsify it - either theoretically or experimentally?

 

[Haelfix]

The measurement issue of quantum mechanics is strictly speaking a distinct and separate problem.

Always in quantum mechanics you have the idea that if you have a state A. Applying the time evolution operator to this state can take you to a new state B.
However, there must exist a sequence of operators that when applied to B, will take you back to A.

In the case of a black hole, you have a state of the universe called A. Some time later (time evolution is applied to A), stellar collapse occurs and you have a new state of the universe B, with a black hole in it. Much later, you have a new state of the universe called C in which the black hole has evaporated.

The problem is, based upon explicit computation, there exists NO sequence of local operators that can ever take this new final state back into the original state A.

This is very different than a measurement process, where you can project a superposition and resolve it. However, you can always 'undo' this process "in principle " (although not always in practice) such that you get back to the original state..

 

[tom.stoer]

You are absolutely right.

Measurement as described in orthodox quantum mechanics with collapse violates unitarity. But Hawking radiation based on QFT plus classical GR violates unitarity entirely on the mathematical level w/o any additional consideration of the measurement problem.

So whereas the measurement problem could be a pseudo-problem created by a specific interpretation of quantum mechanics, the violation of unitarity due to Hawking radiation is indeed a serious problem.

 

[Fra]

So whereas the measurement problem could be a pseudo-problem created by a specific interpretation of quantum mechanics, the violation of unitarity due to Hawking radiation is indeed a serious problem.

On the surface i of course agree they are separate things.

But my own understanding have evolved into beeing sure they are related. I even think gravity and spacetime itself will emerge from the picture of interacting processing agents once we have a reconstructed measurement theory.

As this is my ambition i do not see any merits in mwi. Nothing wrong with decoherence of course, but it does not solve the problems i want to solve. There are also other problems that are related - where decoherence and mwi says nothing. Unification of forces is what i have in mind.

/Fredrik

 

[Demystifier]

In the information loss paradox, people say that in quantum mechanics , time evolution is unitary. They usually do not say anything about the measurement process of if they do, they briefly say that the measurement process does not violate unitarity either if one takes into account the measuring device . I am guessing they mean by that that the measuring process amounts to entangling the observed state with the measuring device. But I thought that this was controversial, that it assumes a many-world type of interpretation of QM. If I measure the spin of a particle, say, and I get a certain result, surely I cannot deduce the state of the particle before the measurement (other than being able to say that the particle has a nonzero component of the eigenstate corresponding to my measurement).

So what do they mean by saying that in QM, time evolution is *always* unitary??

When they say that evolution is "always" unitary, it should be translated as - always, except perhaps (depending on the interpretation) during a measurement. The point is that evaporation does not seem to be a process of measurement*, so the evolution should be unitary.

*There are attempts to resolve the paradox by arguing that evaporation is a kind of measurement, but it turns out that it can explain only a small fraction of needed information loss. That's because measurement determines only a small fraction of all black-hole information.

 

[martinbn]

The paradox is only a paradox if one insists on unitary evolution. I don't understand why that should be the case! Perhaps the "paradox" should be seen as an indication that QT on curved background should be very different and needs to be modified.

 

[Demystifier]

The paradox is only a paradox if one insists on unitary evolution. I don't understand why that should be the case! Perhaps the "paradox" should be seen as an indication that QT on curved background should be very different and needs to be modified.

Yes, that's a possibility. For instance, I have proposed that ordinary time-evolution unitarity should be abandoned and replaced by a sort of generalized unitarity:
https://arxiv.org/abs/0905.0538
https://arxiv.org/abs/0912.1938
https://arxiv.org/abs/1407.8058

 

[Leo1233783]

I read only 0905.0538, it is very nice and well explained ...
Is this swap not a way to remove the common time properties ? Without this constraint, non physical-time solutions may appear, no ? This might include instantaneous travel between some points as well as an analog symmetric going in reverse time. Or am I missing something ? Sorry if it is too naive. TY

 

[Demystifier]

I read only 0905.0538, it is very nice and well explained ...
Is this swap not a way to remove the common time properties ? Without this constraint, non physical-time solutions may appear, no ? This might include instantaneous travel between some points as well as an analog symmetric going in reverse time. Or am I missing something ? Sorry if it is too naive. TY

I don't understand your question. What common time properties? What constraint? Why do you think that there is possibility for instantaneous travel or reverse time?

Even though I am not certain what do you ask, I suspect that answers to your questions might be implicitly present in my paper https://arxiv.org/abs/gr-qc/0403121 .

For a philosophical perspective see also my http://fqxi.org/community/forum/topic/259 .

 

[Leo1233783]

ok, I'll read your philosophy ...

 

[PeterDonis]

what do they mean by saying that in QM, time evolution is *always* unitary??

I think most of them mean that they are using a no collapse interpretation like the MWI, in which the statement is literally true.

 

[jerromyjon]

I think most of them mean that they are using a no collapse interpretation like the MWI, in which the statement is literally true.

I fail to realize how in any other "interpretation" it wouldn't be true. How, precisely, does collapse dissolve unitary evolution?

 

[PeterDonis]

How, precisely, does collapse dissolve unitary evolution?

Because collapse, in the sense of collapse interpretations (as opposed to how the term is used in, say, the "shut up and calculate" interpretation, where it just means our model is incomplete and is known to be so, and we accept that) explicitly says that the state after measurement is a discontinuous transformation of the state before measurement: you pick one eigenstate out of all the possible ones, using probabilities given by the Born rule, and that becomes the state after measurement. No unitary transformation will do that.